Predicting Electronic Structure in Tricalcium Silicate Phases withImpurities Using First-PrinciplesKayahan Saritas,* Can Ataca, and Jeffrey C. Grossman*

Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, UnitedStates

*S Supporting Information

ABSTRACT: Tricalcium silicate (Ca3SiO5) is heavily used in industry as it is the mostpredominant constituent in Portland cement clinkers. In this work, using ab-initio calculations, weassess the ability of a large selection of substitutions to modify the electronic structure in the M3polymorph of tricalcium silicate. We demonstrate the relation between electronic structure,hybridization of the impurity orbitals, and charge transfer from impurity atoms to the bulk material.Our work suggests that charge localization upon introducing impurities can passivate the reactivesites and several such substitutions are identified.

■ INTRODUCTION

Tricalcium silicate (Ca3SiO5 or C3S) is considered to be themost predominant compound in ordinary Portland cementclinkers, at ∼50−70 wt %.1,2 C3S is usually chemically modifiedupon substituting with impurities, forming a solid solutionwhich is called alite. The amount and content of the impuritiesin C3S can determine the physical and chemical properties ofthe resulting cement such as hydration reactivity,3−5 poly-morphism,1 corrosion resistance,2 and elastic properties.6 Fromthe energy consumption perspective, among other phases incement, producing C3S requires the highest processingtemperature, which accounts for roughly 5% of global CO2emissions.7 As it is also the most reactive, a substantial amountof C3S is necessary to have satisfactory early settingproperties.1,2 Much effort has been spent developing cementusing industrial waste products that can provide the samereactivity properties as ordinary Portland cement clinkers,although these products introduce a wide range of impurities todifferent phases in the cement.8 Although several impuritieshave been found to decrease the reactivity of C3S, thusdecreasing performance even when used in trace amounts, acomprehensive understanding of the chemical behavior ofdifferent impurities in C3S is still lacking.9 Experimental studiesin the field mostly focus on the effect of different impurities byexamining their volatility during production as a measure oftheir incorporation into different phases. However, probingdifferent phases in cement with such impurities can bechallenging, and conflicting results can be open to interpreta-tion due to the complexity of the material itself.10

In this paper, we use quantum mechanical computationalmethods to analyze the structural and electronic properties ofC3S. We examine the changes in the electronic structure, uponintroduction of a wide range of impurities. Such properties ofdifferent substitutions in the dicalcium silicate (Ca2SiO4 orC2S) structure including a preliminary comparison betweenalite and belite (second most compound in portland cement)

structures for the Mg, Al, and Fe substitutions has already beenexamined by Durgun et al.3 In this work we build upon thismethodology and extend the range of impurities investigated inalite substitution. We additionally support these hypotheseswith partial density of states analyses and suggest a relationbetween the electronic structure of some impurities and theiratomic radii.

■ COMPUTATIONAL DETAILS

We performed calculations using density functional theory(DFT),11,12 using the projector augmented plane wavemethod13 (PAW) implemented in the VASP14,15 package.The Perdew−Burke−Ernzerhof (PBE) generalized gradientapproximation16 is used to calculate the exchange correlationenergy with a 500 eV kinetic energy cutoff for the plane wavebasis set. A 4 × 4 × 4 k-point grid centered at the gamma pointis chosen for sampling the Brillouin zone, which was sufficientto converge energies to within 10−5 eV per atom in the unitcell. For supercell calculations the density of k-points was scaledaccordingly. Structural minimization using a conjugate gradientapproach was carried out until the maximum force componenton each atom was smaller than 10−3 eV/Å. For atomic basincharge analysis of the relevant structures, we use the Badercharge analysis.17,18

■ RESULTS AND DISCUSSION

In order to examine the effect of impurities on the C3S phase,we examine its monoclinic M3 (M3-C3S) polymorph, which isconsidered to be the most frequently observed in industrialapplications, constituting 50−70%.1 In this unit cell there are18 Ca, 6 Si, and 30 O atoms19(see Figure S1 in the Supporting

Received: October 21, 2014Revised: January 29, 2015Published: January 30, 2015

Article

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© 2015 American Chemical Society 5074 DOI: 10.1021/jp510597eJ. Phys. Chem. C 2015, 119, 5074−5079

Information). Twenty-four oxygen atoms in the unit cell arebonded to neighboring silicons in a tetrahedral orientation withbond distances of 1.64−1.67 Å, while the remaining six oxygensare ionically bonded to calcium atoms in octahedralcoordination with significaltly longer bond distances of 2.33−2.48 Å. We use the experimental unit cell in ref 19 with latticeparameters a = 12.22 Å, b = 7.08 Å, c = 9.30 Å, and β = 114.93°as the starting unit cell for the ionic relaxation calculationsusing DFT. Our computed lattice parameters yield a = 12.21 Å,b = 7.11 Å, c = 9.23 Å, and β = 116.08°, in good agreement withexperimental data.Within the framework of DFT, the Fukui function has been

generalized from frontier molecular orbital theory of chemicalreactivity to the charge density description for bulk systems.20

Under a constant external potential, ν(r), the Fukui functionf(r) can be described as the change in the electron density ρ(r)at each point r with respect to the differential change in thetotal number of electrons, N, in the system: f(r) = (∂ρ(r)/∂N)ν(r).

21 Because of the well-known derivative discontinuityproblem,22 the Fukui function has one-sided limits when it isapproached from left and right at constant number of totalelectrons. Therefore, electrophilic attack, which causes anelectron decrease in the system, is defined as f−(r) = (∂ρ(r)/∂N)ν(r)

− , and nucleophilic attack which causes an electronincrease in the system is defined as f+(r) = (∂ρ(r)/∂N)ν(r)

+ . Forbulk systems, using the finite difference method, thesequantities can be approximated as the following: f−(r) ≈ρ(r)VBM and f+(r) ≈ ρ(r)CBM, where VBM stands for valenceband maximum and CBM is conduction band minimum.20

It has been shown that the Fukui function can be used toidentify charge localized regions, which can be used to tailorreactive sites in a system.20,22,24 In a similar fashion to frontiermolecular orbital theory, regions where the value of the Fukuifunction is larger will more likely undergo an external chemicalattack and be more reactive than the rest of the system. Thespread of the Fukui function can also provide usefulinformation regarding the degree of localization for chemicalactivity in such sites. It has been reported that the presence ofionically bonded oxygens in C3S yields a higher reactivitycompared to C2S, due to the fact that there are no ionicallybonded oxygen atoms C2S and that covalently bonded silicatetetrahedra in both systems do not influence reactivity.3,4 Withthese findings we can postulate that the reactivity of C3S could

be enhanced by concencrating ρCBM and ρVBM on the ioniccomponents, Ca2+ and O2−, respectively. However, if thesubstitution induces ρCBM and ρVBM to concencrate mostly onimpurity atoms, this will localize the reactive sites on theimpurities and could affect hydration kinetics adversely.Therefore, identifying the impurity atoms which cause heavylocalization on their substitution sites may be useful todetermine impurity atoms that will suppress the reactivity ofalite. We note that the electronic state structure picturepresented here, while useful for gaining understanding of thechanges in reactive sites upon chemical substitution, may notcorrelate directly with the hydration dynamics of the samesurface. For that, dynamical effects that include both chemicalchanges as well as possible surface topological changes must betaken into account, and will be the subject of future work.We examine several doped C3S structures with the impurities

Mg, Al, and Fe, since their oxides are the most prominentlyfound foreign oxides in calcium silicate phases.1 It is reportedthat the maximum amounts of impurities that can be containedin M3-C3S vary with the type of impurity.1 However, we notethat the aim of this study is not to model alite under realisticimpurity concencrations but rather to identify how differentimpurities modify the charge density at the substitution sitesand how this may correspondingly affect the reactivity of thealite phase. Towards this end, we perform direct sitesubstitutions while preserving charge neutrality for all uniquesubstitution cases to find the minimum energy configurations.Previous work on bulk C3S phases using classical force fieldsshowed that although the substitution energy varies with site itdoes not follow a clear trend with substitute atom distance.4

However, it is not possible to identify changes in the chargedensity using classical molecular dynamics methods. Accord-ingly, using DFT, we performed impurity substitutions on thesingle unit cell C3S. Ca

2+ is substituted with Mg2+ and Ca2+ +Si4+ with two Al3+ or two Fe3+ atoms. Our ρVBM and ρCBMresults are shown in Figures 1(a) and 1(b) for pure C3S and,respectively, in 1(c) and 1(d) for Mg substitution, 1(e) and1(f) for Al substitution, and finally 1(g) and 1(h) for Fesubstitution. In pure C3S, ρVBM is localized over ionic oxygens,whereas ρCBM spreads almost evenly throughout the unit cell.This suggests that ionic oxygens are more likely to loseelectrons compared to the rest of the system, and thereforethey will undergo electrophilic attack with cations such as H+,

Figure 1. Band decomposed charge densities at the valence band maximum and conduction band minimum, ρVBM and ρCBM, of M3-C3S for (a),(b)pure; (c),(d) Mg; (e),(f) Al; and (g),(h) Fe doped structures. Green spheres indicate Ca; blue spheres indicate Si; red spheres indicate O; andorange spheres indicate respective impurity atoms in each figure.23

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Na2+, Mg2+, and Ca2+. Since ρCBM is delocalized in pure C3S,there is no distinctive region that is more prone to nucleophilicattack such as OH− and SO4

2−. However, when the Ca2+ issubstituted with Mg2+, the spreads of both ρVBM and ρCBMdecrease slightly, but ρVBM localizes around the ionic oxygensthat are neighboring Mg2+ atoms. The effect is slightly morepronounced for Al3+ substitution. With only these data, it ishard to deduce how these impurities could modify the reactivesites. While the oxygens near the impurities localize the chargearound them which makes them more reactive, they may alsodecrease the number of available reactive sites that coulddecrease the overall reactivity of C3S. In the case of Fe3+

substitution we see stronger localization of charge density inboth ρVBM and ρCBM mainly on the impurity atom, whichsuggests a more definite reduction for the reactivity of this site.In addition to examining the nature of charge localization

over particular sites in doped C3S structures, we also investigatehow the partial density of states (PDOS) responds to doping.With this analysis we can understand which atoms or orbitalscontribute more to the total density of states (DOS) of the C3Scrystal structure near band edges and therefore would be moresusceptible to lose or withdraw electrons. Figure 2 shows that

the DOS for Al- and Mg-doped C3S are similar to the pure C3Selectronic structure, but for Fe-doped C3S, we observe ametallic-like band structure due to the large number of localizedstates formed mostly from Fe d-orbitals near the Fermi energy.When we look at the PDOS for Al- and Mg-doped C3S, weobserve that these two atoms slightly modify the DOS nearboth the conduction and valence bands. Upon substitution, Aland Mg atoms localize the charge density by hybridizing withsurrounding oxygen p-orbitals. The contribution of p-orbitals tothe density of states at the conduction band slightly increases,as can be seen when Figure 2(b), (c), and (d) insets arecompared. This analysis reinforces our findings from the ρVBMand ρCBM profiles that as the impurities undergo strongerhybridization at the conduction band they can have a moredistinctive effect on electronic structure of the reactive sites.

The reason for the modification of the PDOS may be thedifferent charge donation properties of Ca, Mg, and Al in C3Swhich change the bonding between them and the surroundingoxygens, causing accumulation of extra charge on these oxygenp-orbitals.Further examination of the charge transfer of the impurities

with respect to the pure structure can give additional insightregarding their oxidation character and localization of thecharge density in the structure. Bader charge analysis over thepure M3-C3S structure shows that each Ca atom donates 1.55e− on average to the unit cell; each Si atom donates 3.12 e−;each tetrahedral O atom, Oc, withdraws 1.45 e

−; and each ionicO atom, Oi, withdraws 1.54 e

− from the unit cell. In the case ofMg substitution, the Mg atom donates an additional 0.18 e−

charge to the unit cell. This additional charge and enhancementof O p-orbitals around the CBM, as shown in Figure 2(c), canexplain the slight charge localization around the Mg atomobserved in Figure 1(c) and (d). For Al substitution, we have asimilar finding in terms of charge localization as in the Mg case,but each Al atom donates 0.6 e− more to the system, where thereference atoms, Ca + Si, donate 4.67 e− to the structure. Asindicated in Figure 1(e) and (f), in Al substitution the chargedonation is larger and the induced charge localization alsostronger compared to Mg substitution. In the case of Fesubstitution, two Fe atoms donate 2.49 e− in total, decreasingthe amount of charge transferred to the structure by 1.09 e− peratom. Combined with the PDOS analysis in Figure 2(a), we seethat much of the charge has remained on the d-orbitals of Featoms, which can also be deduced from the shape of the chargedensity on Fe in Figure 1(g) and (h), leading to stronglylocalized charge on this impurity. Several experimental studiesregarding Al substitution demonstrate either acceleration25 ordelay26 in hydration reactivity. Similarly, conflicting results forMg-doped alite reactivity are also found, showing either adecrease, increase, or no change in the reactivity.26−28 Thesedifferences could have occurred due to differences in particlesizes, storage conditions, water to solid ratio, and grindingconditions. According to our analysis, upon Mg substitutionwith Ca, the electronic structure of C3S is only slightly altered.Our findings for the Fe substitution are in a good agreementwith experimental studies which have shown that Fe decreasesoverall alite reactivity,27,29 by complete localization of the bothCBM and VBM.Since we already discussed how the electronic structure is

modified when C3S is substituted with Mg, Al, and Fe atoms,we turn our attention to different impurities incorporated intothe M3-C3S unit cell. We consider the following substitutions:(1) one Ca2+ atom with either two +1 oxidation state atoms ina dumbbell orientation or one +2 oxidation state atom, (2) oneCa2+ and one Si4+ atom with either two +3 oxidation stateatoms or group I A and group V A atoms, (3) one Ca2+ and oneO2− with group I A and group VII A atoms, (4) bothtetrahedral and ionic O2− with other group VI A atoms, (5) twoSi4+ atoms with either group III A and group V A atoms or twoother group IV A atoms, and (6) one Si4+ and one O2− atomwith one group III A and one group VII A atoms. In alite,ionically bonded oxygens are more susceptible to deformationthan tetrahedral oxygens, and a defect balancing mechanism isreported as the reorientation of Si tetrahedra, which essentiallyconserves their shape and composition upon substitution.1,4

Therefore, we perform oxygen substitutions only on ionicoxygen sites when more than one atom substitution is made,but nevertheless we also performed substitutions on tetrahedral

Figure 2. Partial density of states for a) Fe, b) Al, c) Mg-doped andthe pure C3S cases. Red, green and cyan lines indicate density of statesprojected on s, p and d orbitals, respectively. The insets of Figure (b),(c) and (d) show the s, p, d partial density of states 8X magnified nearthe conduction band. The dashed red line in each plot shows thelocation of Fermi energy.

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oxygen sites in the case of single oxygen substitutions for thesake of completeness and comparison. The full set of impuritiesthat have been investigated is shown in Figure 3.Differences in charge transfer between the reference atoms in

C3S and the impurities in doped C3S can give rise to theformation of hybridized states and charge localization on theimpurity atom site as discussed in detail for Mg, Al, and Fesubstitutions. In these cases where strong charge localizationoccurs for either the ρVBM or ρCBM, the maximum value of thecharge density (MCD) at the corresponding bands will alsoincrease. Charge will be concentrated in a smaller region,mostly on the impurity and neighboring atoms. Therefore, inorder to quantify the charge localization, η, we introduce a

charge localization function such that η = MCDdoped/MCDpure,where η values close to 1 mean that there is no or weakadditional charge localization compared to pure C3S. In Figure3, we show the localization of ρCBM in the C3S structure with arange of substitutions. We can see from these results that ηCBMfor Fe substitution is found to be the highest among allsubstitution cases considered. This analysis also identifiesseveral other impurities such as As, In, Sn, Ge, Cd, and Hg, assome of the strongest substitution candidates that may localizecharge in C3S. Similar to Fe, these substitutions also heavilylocalize ρCBM, but differently they remain insulating despite adecrease in their band gaps to 2−2.5 eV from 3.98 eV for pureC3S. We have also investigated ηVBM to see how C3S changes

Figure 3. Charge localization on the conduction band minimum, ηCBM, is defined as the maximum charge density value (MCD) of the banddecomposed charge density at the conduction band minimum for doped over pure C3S: ηCBM = MCDdoped/MCDpure. ηCBM values are shown asdifferent impurities indicated on the x-axis are substituted for the respective atoms in pure C3S as indicated in the upper right legend. Oi correspondsto ionic oxygen substitutions, whereas Oc corresponds to covalently bonded oxygen substitutions in pure C3S.

Figure 4. Charge localization over conduction band minimum (ηCBM) versus charge transfer ratio, defined as ρrel = Δρimpurity/Δρreference whereΔρimpurity and Δρreference are the absolute amount of charge transferred from the impurity to the rest of the system and the amount of chargetransferred from the substituted atoms in the reference structure, respectively. The types of substitutions are indicated in the upper right legend.Again, Oi indicates ionicly bonded and Oc indicates covalently bonded oxygen substitutions in pure C3S.

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with substitutions when there is electrophilic chemical attack:however, we conclude that except for Fe there is nosubstitution that modifies ρVBM significantly. Inclusion ofsubstitutions leads to the generation of hybridized statesaround the conduction band but not a significant changearound the valence band. For this reason, we conclude thatηVBM does not change drastically upon substitution.Thus far, we have discussed how charge transfer and charge

localization are closely related. In order to quantify the degreeof charge transfer between the reference C3S and doped C3Sstructures, we define a parameter ρrel = Δρimpurity/Δρreference,such that ρrel corresponds to the absolute amount of chargetransferred from the impurity to the rest of the system,Δρimpurity, divided by the amount of charge that was transferredfrom the substituted atoms in the reference structure, Δρreference.This new parameter, ρrel, plotted in Figure 4 vs η, is useful tounderstand the relation between the localization of the chargeand degree of the charge transfer itself upon substitution. Weobserve that near the region where ρrel is ∼1 significant chargelocalization is not expected. Our charge transfer and PDOSanalysis for Mg, Al, and Fe in Figures 1 and 2 showed thatcharge donation imbalance between atoms that are substitutedchanges the characteristics of the conduction band andtherefore causes charge localization. In the ρrel ≈ 1 case thesubstitute atom has almost the same chemical characteristics asthe substituted atom in pure C3S in terms of charge donation tothe system. However, for substitutions with ρrel smaller than0.8, we start to see a sudden increase in charge localizationvalues for some of the impurities. In this case, the impurityatom holds its charge rather than transferring it to the system,therefore causing charge localization.In addition to modification of the charge density in the

conduction and valence bands, the structural reorganizationupon doping yields several trends which also support the chargelocalization discussion. At the Si site, substitutions with groupsIIIA, IVA, and VA atoms, which increase the size of the oxygentetrahedra in C3S, are also found to localize the charge on theimpurity atom. The atomic radii of impurities at the center ofthe oxygen tetrahedra in C3S, aimpurity, become larger as wemove down in the periodic table, such that aIn > aGa > aAl, aAs >aP > aN, and aSn > aGe > aSi. For that reason, as the distancebetween the impurity atom and the surrounding oxygensincreases, the bonding between them will weaken, and theimpurity atoms will donate less charge to the surroundingoxygen atoms. At the Ca site, there is no definite trend betweenatomic radii and charge localization for all substitutions ingeneral. In the cases with strong charge localization, thenearest-neighbor distance between the impurity and surround-ing O atoms is increased. The lack of such a trend for the caseof the Ca substitution (as compared with Si) may be due to thefact that the Ca−O nearest-neighbor distance is longercompared to the Si−O distance in pure C3S and that theorientation of oxygens around the Ca site is less ordered incomparison to the Si site. This argument also supports ourpreliminary tests in the M1 polymorph of the C3S phase, wherethe results we have are very similar to our results in the M3polymorph. C3S polymorphs are known to be formed bydisplacive transformations, and the main difference that liesbetween these two polymorphs is the relative orientation ofsilicon tetrahedra.30 Therefore, substitutions of differentimpurities are expected to provide similar environments.Although our work attempts to shed light on the chemical

interactions between substitutions in the C3S phase from a

fundamental point of view, as we mentioned additional effectsregarding kinetics of the reactions will also play an importantrole for determining the hydration reactivity.31,32 Surfacereconstruction, solvent effects, and fabrication techniquesshould also be considered in future studies.

■ CONCLUSIONS

We employ density functional theory to analyze the effects of arange of impurities on tricalcium silicate (C3S) phases. Wediscuss the fundamental relation between charge localization ofthe impurities and charge transfer at the substitution site. Weshow that bulk substitutions strongly modify the conductionband minimum by hybridizing with surrounding oxygen atoms,therefore localizing reactive sites on select impurity atoms. Ourcalculations identify several impurities that can reduce thenumber of reactive sites throughout the material, and goodagreement with the available experimental data is demon-strated.

■ ASSOCIATED CONTENT

*S Supporting InformationRelative charge transfer (ρrel) and charge localizationparameters of the CBM (ηCBM) for all impurities in C3Sconsidered in this work; ηCBM vs ρrel figures are shown. Thismaterial is available free of charge via the Internet at http://pubs.acs.org.

■ AUTHOR INFORMATION

Corresponding Authors*E-mail: kayahan@mit.edu*E-mail: jcg@mit.edu

NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTS

This work has been supported by the Concrete SustainabilityHub at MIT, with sponsorship provided by the PortlandCement Association (PCA). Calculations were performed inpart at the National Energy Research Scientific ComputingCenter, which is supported by the Office of Science of the U.S.Department of Energy and in part by the National ScienceFoundation through Teragrid resources provided by TACC.

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